Is a 100 psi oil-less air compressor powerful enough to enable an air drill to remove and tighten lug nuts when changing car tires?
Yes, but you must have an accurate in-line pressure gauge and check it continuously while you hold the tire air chuck in place (do not use a clip-on chuck, as used on foot pumps), or better, a regulator to limit the maximum pressure.
Injuries and even deaths have resulted from over-pressurized tires, particularly during mounting. Smaller tires, such as on bicycles, can be overfilled much more rapidly than car tires... I was present when a friend's bike tire exploded at a service-station pump, and I was unable to hear for minutes afterwards.
I'll assume you're not really using a drill to change tyres.
Air tools like an impact driver (commonly known as windy-gun) usually require 100psi and a good airflow to achieve the high torque required to undo wheel nuts - on a passenger car it should be no problem, on bigger vehicles (4x4, truck, etc.) you need a LOT more torque and it may not work.
However it is not a good idea to tighten your wheel nuts with that device as it has no torque control. If it has enough power to undo your wheel nuts/studs it probably has too much power to put them back on without over-tightening. If it doesn't have the power to undo the nuts/studs then it will not have the power to tighten them safely.
Tightening by hand, ideally using a torque wrench set to the manufacturer's specification, is the way it should be done. Professional wheel & tyre fitting shops use torque wrenches or other devices (including special air tools) which are calibrated to give a safe amount of torque.
I've seen wheel studs have the threads stripped or alloy wheels be damaged when lazy mechanics put the wheels on using an impact driver.